EFFECT OF THE FEEDER CABLE AND TRANSFORMER IMPEDANCE ON THE MECHANICAL OUTPUT CHARACTERISTIC OF THE INDUCTION MOTOR

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1 Intenive Programme Renewable Energy Source May 2011, Železná Ruda-Špičák, Univerity of Wet Bohemia, Czech Republic EFFECT OF THE FEEDER CABLE AND TRANSFORMER IMPEDANCE ON THE MECHANICAL OUTPUT CHARACTERISTIC OF THE INDUCTION MOTOR Ondřej Král ABSTRACT The firt part of thi paper deal with the determination of the equivalent circuit parameter of the induction motor, cable and the tranformer. The econd part of thi paper decribe the effect of the feeder cable impedance on the mechanical output characteritic of the aynchronou motor. Calculation i performed for the ix pole induction motor with the nominal output 20 kw, the feeding tranformer with the rated capacity 50 kva and 630 kva. Calculation i performed by the MATLAB program. KEYWORDS Equivalent circuit, hort circuit tet, no-load tet, mechanical output characteritic, operating condition 1. INTRODUCTION We propoe uitable motor for different tipe mechanical equipment according to the mechanical characteritic of the aynchronou motor and it mechanical load. In modern application motor are controlled by emiconductor converter but ome application with the bigget motor require higher reliability and efficiency. For thee reaon emiconductor converter are not ued for peed-torque controll and thee motor are tarted by direct connection to the power network. Mechanical output characteritic of thee motor are dependend on the impedance of the upply tranfomer and the upply cable. Thi paper preent an example with the aynchronou motor with the output 22 kw, the feeding tranformer with the rated capability 50 kva and the cable interconnection without the cable and with the cable 80 m and 180 m length. 2. CALCULATION OF THE EQUIVALENT CIRCUIT OF THE ASYNCHRONOUS MOTOR AND ITS FEEDING TRANSFORMER 2.1. Equivalent circuit of the aynchronou motor If a motor ha the balanced a magnetic circuit and winding and i upplied by a balanced three-phae voltage, we can decribe it by the ingle-phae equivalent circuit. Leakage inductance (X ta and X rot ) repreent the leak of the magnetic flux. The reitance of the tator winding i marked a Rta in Figure 1. Thi reitance repect Joule loe in the tator winding. Magnetizing inductance X µmo and reitance R Femo are connected in parallel. Inductance X µmo repreent the main magnetizing flux that i in the magnetic circuit of the motor and reitance R FEmo repreent eddy-current loe. 125

2 The rotor reitance eparation between the outgoing mechanical power and Joule loe in the rotor quirrel cage i a function of the lip. Thi dependence i decribed by the equation [1]: 1 = + (1) 1 The left ide of thi equation repreent heat loe in the rotor quirrel cage. The reitance repreent the mechanical power of the motor. The reitance the mechanical power which i: P mech 1 i ued for the calculation of 1 2 = 3 I (2) rot 2.2. Determination of the equivalent circuit parameter by meaurement Element of the aynchnou motor equivalent circuit can be determined by everal meaurement. The firt meaurement i the no-load tet. Thi meaurement determine the magnetizing inductance of the motor (X µmo ) and the reitance R Femo repreent eddy-current loe. During meauring the motor i not mechanically loaded. The econd meaurement i the blocked-rotor tet. Thi meaurement determine the reitance of tator and rotor winding (R ta and R rot ) and leakage inductance of the tator and rotor (X ta and X rot ). During thi meauring the haft of the motor i blocked. The third meaurement i the tator reitance meaurement. Ohm method or ome of the reitance bridge can be ued. Thi meaurement i performed with the aid of direct current. The meaurement of the tranformer i imilar to the meaurement of the aynchronou motor. The magnetizing inductance (X µtr ) and the reitance repreenting the eddy-current loe of the tranformer magnetizing circuit (R Fetr ) are determined by the no-load tet of the tranformer. The tranformer i upplied by nominal voltage and i not loaded. The next meaurement i the hort circuit tet. The meaured tranformer ha a hort-circuited econdary winding and the reduced voltage upplie the primary winding. The reduced upply voltage i elected uch that the nominal current pae through the tranformer. The hort-circuit voltage of the tranformer i recounted into the percentual value. Figure 1 The equivalent circuit of the modelled power ytem 2.3. The parameter of the component ued in the modell Aynchronou motor [1]: Pout = 20 kw U mot = 400 V U kmot = 230 V I kmot = 263 A coϕ k = 0.44 U 0mot = 400 V I 0mot = 17,6 A coϕ 0mot = 0.1 R ta = Ω ix pole The firt feeding tranformer DOTN 50/20 ued in the modell [2]: S tr1 = 50 kva U np1 = 22 kv U n1 = 0.4 V u ktr1 = 3.9 % P ktr1 = 1350 W P 0tr1 = 175 W i 01 = 0.04 I n1 The econd feeding tranformer DOTN 630/20 ued in the modell [2]: S tr2 = 630 kva U np2 = 22 kv U n2 = 0.4 V u ktr2 = 4.1 % P ktr2 = 8400 W P 0tr1 = 1030 W i 01 = 0.04 I n1 126

3 Power network: U n = 22 kv S knwk = 80 MVA Feeding cable: R cab = 3.59 Ω/km X cab = Ω/km U cab = 400 V Length 80 m and 160 m The peed torque characteritic of the ued fan: 4 2 M = n (3) 2.4. Reult of the analye Figure 2 how the influence of the upply network, tranformer and cable impedance on the peedtorque characteritic of the aynchronou motor and the operating point of the motor. The blue curve how the peed-torque characteritic of the motor that i upplied directly by the tranformer (without the cable). The influence of the tranformer and cable on the motor rated operating point i mall. The rated operating point ha ame peed and torque in both cae. The rated capacity of the feeding tranformer ha the great influence on the torque maximum of the motor. Thi moment maximum i important on the electromechanical tranient phenomena. The motor maximum torque increae from 593 Nm to 720 Nm by increae of the feeding tranformer rated capacity from 50 kva to 630 kva. The rated capacity of the feedeng tranformer ha the influence on the tarting torque of the motor. The motor ha the tarting-torque 278 Nm if it i upplied by the feeding tranformer with the rated capacity 50 kva. The motor ha the tarting-torque 370 Nm if it i upplied by the feeding tranformer with the rated capacity 630 kva. Cable with 80 m and 160 m length decline the tartingtorque and the maximum torque of the motor. The high impedance (the mall feeding tranformer or the length feeding cable) in front of the motor may lead to the untability of the motor tarting. The torque generated by the motor i le than the load torque. Figure 2 Speed-Torque characteritic of the aynchronou motor (20 kw) that i powered by two tranformer (50 kva - left, 630 kva - right) The third figure how a plot of the mechanical output veru the motor rotating peed during the tarting of the motor. The rotating peed i equal to zero at the firt time after the tart of the motor (the lip of the motor equal to one) hence the outgoing mechanical power i zero. The value of the motor outgoing mechanical power deignate the tarting time of the motor. If the outgoing mechanical power ha the greate value, the motor tarting time i hort. The power peak i reduced by the impedance of the feeding tranformer and the cable. When the motor peed approache the ynchronou peed, the motor output mechanical power i zero becaue the motor ha not any torque. In thi cae the tator input current pae through the magnetizing inductance. The input tarting apperent power of the motor can be even time higher than the input rated apperent power. 127

4 Figure 3 Dependence of the mechanical power on the motor peed of the aynchronou motor (20 kw) that i powered by two tranformer (50 kva - left, 630 kva - right) An input current veru the motor peed i hown in figure four. Thi characteritic how the influence of the feeding tranformer rated capacity on the input tarting current. The tarting current value i important to etting up of the motor electrical protection and deign of the feeding ource rated capacity. If the ued motor (20 kw) i upplied by the tranformer (without the cable) with the rated capacity 50 kva it tarting current i 228 A. The motor ha the trating current 263 A if the feeding tranformer with the rated capacity 630 kva i ued. By the ynchronou peed of the motor i paing current through the motor 17 A. Thi current pae through the magnetizing inductance and it i almot independent on the impedance in front of the motor. Figure 4 Dependence of the upplied current on the motor peed of the aynchronou motor (20 kw) that i powered by two tranformer (50 kva - left, 630 kva - right) The value of the feedeing tranformer rated capacity ha the greate influence on the motor terminal voltage by the tart of the motor. The terminal voltage of the motor i important to the determinating of the torque maximum of the peed-torque characteritic. The terminal voltage of the motor veru the motor peed i hown in figure five. If the tranformer with the rated capacity 630 kva upplie (without cable) the motor, it line to line terminal voltage by the tart i 394 V. It i very mall voltage reduction. If the motor i upplied by the tranformer with the rared capacity 50 kva, the line to line voltage reduction i 57 V by the tart. Thi voltage reduction can adverely affect other equipment connected to the ame tranformer. The high value of the feeding tranformer (or cable) impedence induce thi large voltage reduce. 128

5 Figure 5 Dependence of the terminal voltage on the motor peed of the aynchronou motor (20 kw) that i powered by two tranformer (50 kva - left, 630 kva - right) 3. CONCLUSIONS Above the reult indicate influence the value of the impedance in front of the motor on the mechanical output power and the influence on the electrical unit (input current, input apparent power, terminal voltage). We can ue thee reult for deign of the motor and the tranformer protection. The aynchrnou motor have other propertie by the tarting and other propertie in nominal oparation. We have to deign of the feeding ource and the feeding line in the light of the tranient phenomena of the motor. If the motor i upplied by the thanformer with the low rated capacity, the voltage reduction can be dangerou for other equipment. Above the characteritic can be ued for the teaching. REFERENCES [1] Bašta, Jan; Chládek, Jarolav; Mayer, Imrich: Teorie elektrických trojů. Praha SNTL 1968 [2] ACKNOWLEDGMENT Thi work wa upported and granted by project no. SGS Author: Ing. Ondřej Král Univerity of Wet Bohemia Department of Electrical Power Engineering and Environmental Engineering Univerzitní 8, Plzeň, Czech Republic ondrej@kee.zcu.cz 129